Mayor Thomas M. Menino, respond­ing to demand from families for more downtown schools, will announce a plan Friday to open a new school in the North End, tapping a waterfront building that once housed Mitt Romney’s presidential campaign headquarters.

By purchasing 585 Commercial St. and renovating it,
the city will be able to accom­modate about 500 students in kindergarten through Grade 8, city officials said. The school is ­expected to open by September 2016.

Menino said the announcement marks another step in the city’s ­effort to let more children attend schools closer to their homes.

“Having so many young families who want to live downtown and send their children to a Boston public school says a lot about our city and a lot about our school system,” Menino said in a statement. ­“Today’s downtown isn’t just a place where people come to work; it’s a real community where people want to live and raise their families.”

Renovation of the building would not begin immediately. ­Initially, the building will be used to house several grades from the Eliot K-8 School in the North End, while a second campus for that school is renovated as part of an expansion. Once the Eliot project is completed, the city would renovate 585 Commercial St.

The mayor still needs City Council approval to spend $12.85 million to buy the three-story, 42,000-square-foot building. He also will need permission from the School Committee, which he appoints, to open a new school.

On Wednesday night the School Committee took a huge step toward that approval when it adopted a new school assignment plan that includes a commitment to open a school somewhere in the downtown vicinity.

The effort is the latest in a series over the last decade to open a new downtown school. In 2009 a developer proposed building a school in Government Center as part a massive redevelopment project, and in 2003, a group of Beacon Hill parents tried to persuade Menino and school officials to purchase a building on Brimmer Street
and make it a public school, even offering to raise money. Both proposals were rejected.

A few months ago, downtown parents renewed their push, as the city held public meetings on changing the way it assigns students to schools so that more of them could attend one close to home.

In launching their campaign for a new school, parents have repeatedly stressed that there are no public elementary schools or K-8 schools in the Back Bay, Beacon Hill, Downtown Crossing, or the West End, the result of a wave of school closings many years ago when families were fleeing the city. The closest schools are in the North End, Chinatown, and the South End.

Although the mayor’s plan does not locate a school in a neighborhood without one, downtown school proponents still welcomed the news, albeit with a cautionary note.

“This shows the mayor and the School Committee are fulfilling, finally, the promises they made to serve families who live downtown, but we are going to need more than this one location, because so many parents want to send their children to the Boston public schools,” said Marty Walz, a former state representative who helped to organize the non­profit Downtown Schools for Boston a few months ago.

Still, she said, “This is a positive development.”

Built in the 1960s by the federal government, the Commercial Street building initially housed the US Food and Drug Administration, then the law firm Prince Lobel Glovsky & Tye and the high-end home furnisher Roche-Bobois.

When Romney moved into the building in late 2006, a ­developer had plans to raze it to make way for an eight-story luxury condominium tower, but he hit oppostion from North End residents worried about accelerating gentrification.

Competition to get into the new school is expected to be stiff. The number of residents ­under the age of 18 in downtown neighborhoods has ­increased by 25 percent in the last decade, according to census data. That population in 2010 was 2,620, compared with 2,091 in 2000.

Downtown families also will probably vie for slots against families in East Boston, another part of the city with a shortage of school seats. Commercial Street is just a short distance from tunnels to and from East Boston, so families there may find the new school an appealing alternative. It also is close to the Charlestown Bridge, potentially drawing families over there.

Councilor Michael Ross, who represents the downtown area, expressed optimism that a school will finally arrive.

“This is a long time coming,” Ross said. “Long ago, downtown families — it was almost an anomaly to consider attending a public school. A lot of families had given up on public education.

“But over the last 10 years or so that has changed,” he said. “We have seen a real hunger from downtown families to send their children to the ­Boston public schools.”